流体在可渗透壁面上的统计力学
Statistical mechanics of fluids at a permeable wall
摘要：
研究了有限力场作用下流体边界的表面效应问题。考虑了一个经典的简单流体与一个局部引入的领域模仿可渗透固体。考察了微观和宏观光滑边界的情况，并对静态膜进行了分析。测定了吸附亨利常数及其与亨利常数、比表面巨势和表面数密度的关系。得到了基本值的高温膨胀和低温极限。“表面张力系数“分解为取决于分离表面的位置的与吸附的亨利常数成比例的值和通用的非线性表面系数。两种方法来解决这个问题进行了分析：通过表面团簇膨胀和通过压力张量。在第一种方法中，获得伽马的活度幂级数。该表达式类似于压力的簇展开，但与此相反，Ursell因子的积分包含取决于粒子与外场相互作用的势的乘数。在第二种方法中，Kirkwood-Buff公式伽玛的情况下，有限值的字段进行了扩展。证明了“团簇展开”和“压力张量”方法的完全一致性，并构造了确定近表面区域“二维”气体精确状态方程的近表面维里展开。重合的压力作用在一个横向的壁和切向分量的压力张量，这两个平均过渡层，以及对称的解决方案相对于置换的吸附剂-流体的演示。
英文摘要：
The problem of surface effects at a fluid boundary created by the force field of finite value is investigated. A classical simple fluid with a locally introduced field imitating a permeable solid is considered. The cases of micro- and macroscopically smooth boundary are examined and the analysis of static membranes is performed. Henry constant of adsorption and its connection with Henry constant of absorption, specific surface grand potential (gamma) and the surface number density are determined. High-temperature expansions and low-temperature limit for basic values are obtained. "The surface tension coefficient" decomposes into a value proportional to Henry constant of adsorption depending on the position of the separating surface, and a universal nonlinear surface coefficient. Two approaches to this problem are analyzed: through the surface cluster expansion and through the pressure tensor. Within the first approach, the series in powers of activity is obtained for gamma. This expression is similar to the cluster expansion for pressure but in contrast to this case the integrals of Ursell factors contain the multipliers depending on the potential of particles interaction with the external field. Within the second approach, Kirkwood-Buff formula for gamma is extended for the case of the field of finite value. A complete identity of the approaches of "cluster expansion" and "pressure tensor" is demonstrated, and the near-surface virial expansion which determines the exact equation of state of the "two-dimensional" gas of the near-surface region is constructed. Coincidence of pressure acting on a transverse wall and the tangential component of pressure tensor, both averages over the transition layer as well as the symmetry of the solution with respect to the permutation of sorbent - fluid are demonstrated.
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